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<title>sun123zxy&#39;s blog</title>
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<item>
  <title>On the Number of 3-Part Stable Partitions of the Half Graph</title>
  <dc:creator>sun123zxy </dc:creator>
  <link>https://blog.sun123zxy.top/posts/20250505-hn-chromatic/</link>
  <description><![CDATA[ Disclaimer: Results below are original and not formally verified. Stay sharp for potential mistakes. ]]></description>
  <category>math</category>
  <category>combinatorics</category>
  <category>solution</category>
  <guid>https://blog.sun123zxy.top/posts/20250505-hn-chromatic/</guid>
  <pubDate>Sun, 04 May 2025 00:00:00 GMT</pubDate>
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  <title>【BICMR 怀新一题】人偶之舞 题解</title>
  <dc:creator>sun123zxy </dc:creator>
  <link>https://blog.sun123zxy.top/posts/20250117-doll/</link>
  <description><![CDATA[ <span class="theorem-title"><strong>例 1</strong></span> 寻找各人偶速度 <img src="https://latex.codecogs.com/png.latex?v_1,%5Cdots,v_m%20%5Cin%20%5Cmathbb%20R%20/%20%5Cmathbb%20Z">，使得对任意的人偶起始位置 <img src="https://latex.codecogs.com/png.latex?a_1,%5Cdots,a_m%20%5Cin%20%5Cmathbb%20R%20/%20%5Cmathbb%20Z">，存在数列 <img src="https://latex.codecogs.com/png.latex?N_k%20%5Csubseteq%20%5Cmathbb%20N"> 使得 Shanghai 人偶旋转 <img src="https://latex.codecogs.com/png.latex?N_k"> 圈后，各人偶位置 <img src="https://latex.codecogs.com/png.latex?x_%7Bi,N_k%7D%20:=%20a_i%20-%20N_k%20v_i"> 满足 <img src="https://latex.codecogs.com/png.latex?%0A%20%20%5Cmax_%7B1%20%5Cleq%20i%20%5Cleq%20m%7D%20%7Cx_%7Bi,N_k%7D%7C%20=%20O(N_k%5E%7B-1/m%7D),%20%5Cquad%20k%20%5Cto%20%5Cinfty%0A%20%20"> 这里 <img src="https://latex.codecogs.com/png.latex?%7C%20%5Ccdot%20%7C"> 表示与 <img src="https://latex.codecogs.com/png.latex?0"> 在 <img src="https://latex.codecogs.com/png.latex?%5Cmathbb%20R%20/%20%5Cmathbb%20Z"> 中的距离． ]]></description>
  <category>math</category>
  <category>analysis</category>
  <category>number theory</category>
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  <guid>https://blog.sun123zxy.top/posts/20250117-doll/</guid>
  <pubDate>Fri, 17 Jan 2025 00:00:00 GMT</pubDate>
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  <title>【ICPC 2024 Regional 昆明热身赛 D】LCA Determinant 题解</title>
  <dc:creator>sun123zxy </dc:creator>
  <link>https://blog.sun123zxy.top/posts/20241130-lcadet/</link>
  <description><![CDATA[ 热身赛 D 供题人．原题出自 <a href="https://codeforces.com/gym/104825/problem/H">2023 年 BIT 校赛 H</a>，非常荣幸被组题人收入热身赛供大家把玩．看到很多人对题目背后的动机感兴趣，也把题解放到这里，趁机聊聊此类行列式背后的技巧和理论． ]]></description>
  <category>math</category>
  <category>algorithm</category>
  <category>combinatorics</category>
  <category>original problem</category>
  <category>solution</category>
  <guid>https://blog.sun123zxy.top/posts/20241130-lcadet/</guid>
  <pubDate>Sat, 30 Nov 2024 00:00:00 GMT</pubDate>
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  <title>str 学数学 题解</title>
  <dc:creator>sun123zxy </dc:creator>
  <link>https://blog.sun123zxy.top/posts/20230213-strwithmath/</link>
  <description><![CDATA[ <span class="theorem-title"><strong>Example 1 (str 学数学)</strong></span> str 同学因为名字里含有一个 str，所以觉得字符串对于他来说太简单了，于是他开始了他的数学之旅。 ]]></description>
  <category>algorithm</category>
  <category>math</category>
  <category>number theory</category>
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  <guid>https://blog.sun123zxy.top/posts/20230213-strwithmath/</guid>
  <pubDate>Mon, 13 Feb 2023 00:00:00 GMT</pubDate>
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  <title>关于泰勒展开拉格朗日余项中值点的渐进性</title>
  <link>https://blog.sun123zxy.top/posts/20221110-taylor/</link>
  <description><![CDATA[ 之前学拉格朗日中值定理的时候做到一道涉及到特定函数中值渐进性的题，感觉似乎有一般的结论，推广了一下就是这样了。 ]]></description>
  <category>math</category>
  <category>analysis</category>
  <category>solution</category>
  <guid>https://blog.sun123zxy.top/posts/20221110-taylor/</guid>
  <pubDate>Wed, 02 Nov 2022 00:00:00 GMT</pubDate>
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<item>
  <title>原创OI题目 GCD卷积 Problem and Solution</title>
  <link>https://blog.sun123zxy.top/posts/20201206-gcdconv/</link>
  <description><![CDATA[ 比赛用题面、题解、标程和数据生成器均已挂在 <a href="https://github.com/sun123zxy/gcdconv">git@github.com:sun123zxy/gcdconv.git</a> 上。 ]]></description>
  <category>algorithm</category>
  <category>math</category>
  <category>combinatorics</category>
  <category>original problem</category>
  <category>solution</category>
  <guid>https://blog.sun123zxy.top/posts/20201206-gcdconv/</guid>
  <pubDate>Sun, 06 Dec 2020 00:00:00 GMT</pubDate>
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  <title>原创OI题目 白银之春 Problem and Solution</title>
  <link>https://blog.sun123zxy.top/posts/20201206-spring/</link>
  <description><![CDATA[ 比赛用题面、题解、标程和数据生成器都挂在 <a href="https://github.com/sun123zxy/spring">git@github.com:sun123zxy/spring.git</a> 上。 ]]></description>
  <category>algorithm</category>
  <category>original problem</category>
  <category>solution</category>
  <guid>https://blog.sun123zxy.top/posts/20201206-spring/</guid>
  <pubDate>Sun, 06 Dec 2020 00:00:00 GMT</pubDate>
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<item>
  <title>卡特兰数 题解</title>
  <link>https://blog.sun123zxy.top/posts/20201204-catalan/</link>
  <description><![CDATA[ <a href="https://oj.bashu.com.cn/code/problempage.php?problem_id=7107">bsoj7107</a> ，来源不明。 ]]></description>
  <category>algorithm</category>
  <category>combinatorics</category>
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  <guid>https://blog.sun123zxy.top/posts/20201204-catalan/</guid>
  <pubDate>Fri, 04 Dec 2020 00:00:00 GMT</pubDate>
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  <title>树的解构 题解</title>
  <link>https://blog.sun123zxy.top/posts/20201127-deconstruct/</link>
  <description><![CDATA[ <a href="https://oj.bashu.com.cn/code/problempage.php?problem_id=7076">bsoj7076</a>，没找到出处… ]]></description>
  <category>algorithm</category>
  <category>probability</category>
  <category>math</category>
  <category>solution</category>
  <guid>https://blog.sun123zxy.top/posts/20201127-deconstruct/</guid>
  <pubDate>Fri, 27 Nov 2020 00:00:00 GMT</pubDate>
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<item>
  <title>CodeChef-LECOINS Little Elephant and Colored Coins 题解</title>
  <link>https://blog.sun123zxy.top/posts/20201118-coin/</link>
  <description><![CDATA[ <a href="https://www.codechef.com/problems/LECOINS">CodeChef-LECOINS Little Elephant and Colored Coins</a> ]]></description>
  <category>algorithm</category>
  <category>solution</category>
  <guid>https://blog.sun123zxy.top/posts/20201118-coin/</guid>
  <pubDate>Wed, 18 Nov 2020 00:00:00 GMT</pubDate>
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<item>
  <title>CodeChef-RNDRATIO Mysterious Ratio 题解</title>
  <link>https://blog.sun123zxy.top/posts/20201116-ratio/</link>
  <description><![CDATA[ <a href="https://www.codechef.com/problems/RNDRATIO">CodeChef-RNDRATIO Mysterious Ratio</a> ]]></description>
  <category>algorithm</category>
  <category>math</category>
  <category>number theory</category>
  <category>solution</category>
  <guid>https://blog.sun123zxy.top/posts/20201116-ratio/</guid>
  <pubDate>Mon, 16 Nov 2020 00:00:00 GMT</pubDate>
</item>
<item>
  <title>树上差分的两种形式（相遇 or 行程的交集 题解）</title>
  <link>https://blog.sun123zxy.top/posts/20201024-treediff/</link>
  <description><![CDATA[ emm，这很NOIP… ]]></description>
  <category>algorithm</category>
  <category>solution</category>
  <guid>https://blog.sun123zxy.top/posts/20201024-treediff/</guid>
  <pubDate>Sat, 24 Oct 2020 00:00:00 GMT</pubDate>
</item>
<item>
  <title>浅析一类要求相邻不同的环上染色问题</title>
  <link>https://blog.sun123zxy.top/posts/20200204-circle/</link>
  <description><![CDATA[ 我们先来解决最经典的圆环染色问题。 ]]></description>
  <category>algorithm</category>
  <category>math</category>
  <category>combinatorics</category>
  <category>solution</category>
  <guid>https://blog.sun123zxy.top/posts/20200204-circle/</guid>
  <pubDate>Tue, 04 Feb 2020 00:00:00 GMT</pubDate>
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<item>
  <title>bsoj5988 [Achen模拟赛]期望 题解</title>
  <link>https://blog.sun123zxy.top/posts/20191218-mex/</link>
  <description><![CDATA[ <a href="https://oj.bashu.com.cn/code/problempage.php?problem_id=5988">bsoj5988</a> ]]></description>
  <category>algorithm</category>
  <category>math</category>
  <category>number theory</category>
  <category>combinatorics</category>
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  <guid>https://blog.sun123zxy.top/posts/20191218-mex/</guid>
  <pubDate>Wed, 18 Dec 2019 00:00:00 GMT</pubDate>
</item>
<item>
  <title>涂色游戏 题解</title>
  <link>https://blog.sun123zxy.top/posts/20191209-paint/</link>
  <description><![CDATA[ <a href="https://oj.bashu.com.cn/code/problempage.php?problem_id=6412">bsoj6412</a> 没找到出处。。。 ]]></description>
  <category>algorithm</category>
  <category>math</category>
  <category>combinatorics</category>
  <category>probability</category>
  <category>solution</category>
  <guid>https://blog.sun123zxy.top/posts/20191209-paint/</guid>
  <pubDate>Mon, 09 Dec 2019 00:00:00 GMT</pubDate>
</item>
<item>
  <title>[JZOJ A组]球 题解</title>
  <link>https://blog.sun123zxy.top/posts/20191012-ball/</link>
  <description><![CDATA[ 首先看到<img src="https://latex.codecogs.com/png.latex?10%5E7">的数据和仅有2个参数的较多询问，马上想到这是一道和预处理阶乘有关的题。 ]]></description>
  <category>algorithm</category>
  <category>math</category>
  <category>combinatorics</category>
  <category>probability</category>
  <category>solution</category>
  <guid>https://blog.sun123zxy.top/posts/20191012-ball/</guid>
  <pubDate>Sat, 12 Oct 2019 00:00:00 GMT</pubDate>
</item>
<item>
  <title>由 [SDOI2012]Longge的问题 探讨欧拉函数和莫比乌斯函数的一些性质和关联</title>
  <link>https://blog.sun123zxy.top/posts/20190922-muphi/</link>
  <description><![CDATA[ 题目传送门：<a href="https://www.luogu.org/problem/P2303">https://www.luogu.org/problem/P2303</a> ]]></description>
  <category>algorithm</category>
  <category>math</category>
  <category>number theory</category>
  <category>solution</category>
  <guid>https://blog.sun123zxy.top/posts/20190922-muphi/</guid>
  <pubDate>Sun, 22 Sep 2019 00:00:00 GMT</pubDate>
</item>
<item>
  <title>[NOIP模拟]文本编辑器 题解</title>
  <link>https://blog.sun123zxy.top/posts/20190828-editor/</link>
  <description><![CDATA[ <a href="https://oj.bashu.com.cn/code/problempage.php?problem_id=5089">bsoj5089 文本编辑器</a> ]]></description>
  <category>algorithm</category>
  <category>solution</category>
  <guid>https://blog.sun123zxy.top/posts/20190828-editor/</guid>
  <pubDate>Wed, 28 Aug 2019 00:00:00 GMT</pubDate>
</item>
<item>
  <title>洛谷P5364 [SNOI2017]礼物 题解</title>
  <link>https://blog.sun123zxy.top/posts/20190701-gift/</link>
  <description><![CDATA[ <a href="https://www.luogu.com.cn/problem/P5364">传送门</a> ]]></description>
  <category>algorithm</category>
  <category>math</category>
  <category>combinatorics</category>
  <category>solution</category>
  <guid>https://blog.sun123zxy.top/posts/20190701-gift/</guid>
  <pubDate>Mon, 01 Jul 2019 00:00:00 GMT</pubDate>
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